Problem: Simplify the following expression: $x = \dfrac{-7z + 70}{-42z + 21}$ You can assume $z \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-7z + 70 = - (7 \cdot z) + (2\cdot5\cdot7)$ The denominator can be factored: $-42z + 21 = - (2\cdot3\cdot7 \cdot z) + (3\cdot7)$ The greatest common factor of all the terms is $7$ Factoring out $7$ gives us: $x = \dfrac{(7)(-z + 10)}{(7)(-6z + 3)}$ Dividing both the numerator and denominator by $7$ gives: $x = \dfrac{-z + 10}{-6z + 3}$